Effective generating functions for quantum canonical transformations

Journal Article · Sun Feb 15 04:00:00 EST 1987 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.35.1289· OSTI ID:6767285

Ghandour, G I

An effective generating function F(q,Q) is introduced for any given pair of quantum-mechanical systems whose classical Hamiltonians are canonically equivalent. Using e/sup i//sup F/ as a kernel, an integral transform relates the wave functions of the corresponding quantum systems. The function F reduces in the classical limit (h-dash-bar..-->..0) to the generating function of the classical transformation. Conversely, starting with the classical form, F can be calculated in a recurrent fashion, order by order in powers of h-dash-bar. For the canonical transformation that relates a particle moving in an exponential (Liouville) potential to a free particle, the effective quantum generating function is identical to its classical counterpart. The generalization to quantum field theory is possible using the Schroedinger wave-functional formalism.

• Research Organization: Department of Physics, Kuwait University, Kuwait
• OSTI ID: 6767285
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 35:4; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CANONICAL TRANSFORMATIONS
CLASSICAL MECHANICS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONS
HAMILTONIANS
MATHEMATICAL OPERATORS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
TRANSFORMATIONS
WAVE EQUATIONS
WAVE FUNCTIONS